Best for
Years 4-6 students beginning to use the language of probability and connect “likely” and “unlikely” with simple fractions and everyday events.
Pāngarau / Mathematics • Statistics • Years 4-6
Probability Basics: Chance in Everyday Aotearoa
Probability helps us describe how likely something is to happen. This handout gives ākonga a clear chance scale, everyday event sorting, and simple probability questions using words, fractions, and common sense.
Free class-ready resource, premium progression path
This version is designed for immediate classroom use. If you want a localised sequence, bilingual prompts, or assessment-ready follow-up tasks, Te Wānanga can expand it without losing the print simplicity.
- Generate entry, on-level, and extension versions.
- Swap in local school, weather, or sport contexts.
- Save your adapted probability sequence in My Kete.
Kaiako planning snapshot
- Use length: 30-40 minutes.
- Grouping: Whole-class warm-up, then independent or paired practice.
- Prep: Optional coin, die, or spinner for a concrete starter.
- Teaching move: Keep probability grounded in the words students already use: impossible, unlikely, even chance, likely, certain.
Resources already provided
- Probability scale
- Event-sorting task
- Simple fraction questions
- Explanation space
- Teacher-only curriculum companion
The handout works with or without physical equipment.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how to describe chance using probability language.
- We are learning how to represent simple probability as a fraction.
- We are learning how to justify why one event is more or less likely than another.
Paearu Angitu / Success Criteria
- I can place events on the chance scale sensibly.
- I can calculate a simple probability from the number of outcomes.
- I can explain my thinking using words and numbers.
Curriculum integration / Te Mātaiaho alignment
This handout supports the early probability language and concepts students need before moving into richer chance investigations and comparison tasks.
Why this matters in Aotearoa
Probability shows up in weather reports, games, class sports, road safety, and everyday decisions. Students need to see chance as more than guesswork; it is a way of describing how likely something is, based on known possibilities.
Keep the contexts grounded and age-appropriate. In te ao Māori, close observation of weather, season, and environment also matters, so everyday examples should connect chance language to careful noticing rather than trivia or magical guessing.
The chance scale
0 Impossible
1/2 Even chance
1 Certain
Impossible
Unlikely
Even chance
Likely
Certain
Place each event on the scale
| Event | Where does it fit? | Why? |
|---|---|---|
| Rolling a 7 on a six-sided die | ||
| Flipping heads on a fair coin | ||
| The sun rising tomorrow | ||
| Rain sometime in Tāmaki Makaurau this winter |
Simple probability problems
1. Kete counters
A kete has 4 blue counters and 2 yellow counters. What is the probability of picking a yellow counter?
2. Spinner
A spinner has 8 equal sections. Two sections are koru, three are stars, and three are waves. What is the probability of landing on a koru?
3. Dice
What is the probability of rolling an even number on a fair die?
4. Compare
Which is more likely: rolling a 6 on a die or picking a yellow counter from the kete above? Explain why.
Show it in words and numbers
One event I would describe as unlikely is...
One event I would describe as an even chance is...
Support
Use real objects first, then translate to words like impossible and likely before asking for fractions.
Core
Students place events on the scale and solve simple probability questions independently.
Stretch
Ask students to invent their own equally likely experiment and explain the possible outcomes.
Neurodiversity and inclusion note
Let students talk, point, or sort physically before writing fractions. The conceptual language of chance often lands first through concrete action.
Kaiako reminder
Keep probability grounded in equally likely outcomes. Students should not be forced into vague guesses when the event structure can be made explicit.
Hononga Marautanga · Curriculum Alignment
Mathematics — Pāngarau
Level 3–4: Apply number operations, statistical analysis, and mathematical reasoning to solve real-world problems; represent data using appropriate tools; interpret and communicate mathematical findings clearly.
Social Sciences — Tikanga ā-Iwi
Level 3–4: Understand how mathematical data and statistics are used to describe and analyse social, economic, and environmental patterns; recognise how data can reveal or obscure inequality.
Aronga Mātauranga Māori
Mathematics has always been part of mātauranga Māori — in the navigation of Te Moana-nui-a-Kiwa, in the architectural precision of wharenui, in the sophisticated storage and accounting systems of rua kūmara, and in the patterns of kōwhaiwhai and tukutuku that encode mathematical relationships in visual form. When Māori students engage with mathematics, they are not encountering something foreign: they are meeting a domain of knowledge that their tīpuna practised with extraordinary sophistication. Framing mathematical learning through whakapapa — connecting concepts to real Māori contexts — is not "cultural add-on" but recognition of where much mathematical knowledge lives in this land.
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. Related resources from the same unit are linked in the unit planner. All resources are provided — no additional preparation is required to use this handout in your classroom.
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to build pāngarau (mathematical) understanding — developing number sense, pattern recognition, and mathematical reasoning through hands-on, culturally grounded activities that connect to tamariki's world.
Ngā Paearu Angitū — Success Criteria
- ✅ Students can explain their mathematical thinking using words, objects, drawings, or symbols.
- ✅ Students can apply the number or pattern concept in this resource to a real or everyday context.
Differentiation & Inclusion
Scaffold support: Use concrete materials (blocks, counters, fingers) for entry-level engagement before progressing to abstract representations. Offer extension challenges asking students to generalise a pattern, write their own word problem, or explain their strategy to a partner.
ELL / ESOL: Mathematical language is a discipline-specific barrier — pre-teach key terms (e.g., equals, more than, fewer, pattern, factor) using visual representations. Allow students to demonstrate mathematical understanding non-verbally or through drawing. Pair with a bilingual buddy where possible.
Inclusion: Embed choice in how students engage — oral, written, or diagrammatic responses are all valid. Neurodiverse learners benefit from short, chunked task sequences with immediate feedback loops. Avoid timed drills in favour of exploratory tasks that reward curiosity. Make the maths classroom a safe place to be wrong and try again.
Mātauranga Māori lens: Pāngarau is a living tradition in Te Ao Māori — from the geometric precision of tukutuku and kōwhaiwhai patterns to the navigational mathematics of waka hourua, and the seasonal calculations embedded in maramataka. Framing early number sense within these contexts shows tamariki that mathematics is a human, culturally rich endeavour — not a foreign import. Encourage students to see counting, measuring, and patterning as acts of knowing their world.
Prior knowledge: Designed for early learners. No prior formal mathematics knowledge required. Teachers should assess current number knowledge before selecting appropriate entry points.
Curriculum alignment
- Number and Algebra — Number Strategies: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
- Number and Algebra — Patterns and Relationships: Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.